The fractal image coding technique has attracted a degree of interest for its low bit rate. But the reconstructed image is of medium quality. This problem has prevented the fractal technique from being practically used. In order to improve the compression fidelity, a new affine ransformation is roposed in this paper. Meanwhile, its contractivity requirement is analyzed, and the optimal parameters are derived using the least square method. The new affine transformation has been practically used in image coding. Experiments show that the PSNR can reach 28.7dB at a compression ratio (CR) of 16.4 for the 256 256 8 "Lena" image. Comparison with other fractal coding schemes shows that the new affine transformation can improve the reconstructed image quality efficiently.